Eric Pichon

Finsler Active Contours

In this paper, we propose an image segmentation technique based on augmenting the conformal (or geodesic) active contour framework with directional information. In the isotropic case, the euclidean metric is locally multiplied by a scalar conformal factor based on image information such that the weighted length of curves lying on points of interest (typically edges) is small. The conformal factor that is chosen depends only upon position and is in this sense isotropic. Although directional information has been studied previously for other segmentation frameworks, here, we show that if one desires to add directionality in the conformal active contour framework, then one gets a well-defined minimization problem in the case that the factor defines a Finsler metric. Optimal curves may be obtained using the calculus of variations or dynamic programming-based schemes. Finally, we demonstrate the technique by extracting roads from aerial imagery, blood vessels from medical angiograms, and neural tracts from diffusion-weighted magnetic resonance imagery.

Mathematical methods in medical image processing

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation.

A hamilton-jacobi-bellman approach to high angular resolution diffusion tractography

This paper describes a new framework for white matter tractography in high angular resolution diffusion data. A direction-dependent local cost is defined based on the diffusion data for every direction on the unit sphere. Minimum cost curves are determined by solving the Hamilton-Jacobi-Bellman using an efficient algorithm. Classical costs based on the diffusion tensor field can be seen as a special case. While the minimum cost (or equivalently the travel time of a particle moving along the curve) and the anisotropic front propagation frameworks are related, front speed is related to particle speed through a Legendre transformation which can severely impact anisotropy information for front propagation techniques. Implementation details and results on high angular diffusion data show that this method can successfully take advantage of the increased angular resolution in high b-value diffusion weighted data despite lower signal to noise ratio.

A statistically based flow for image segmentation

In this paper we present a new algorithm for 3D medical image segmentation. The algorithm is versatile, fast, relatively simple to implement, and semi-automatic. It is based on minimizing a global energy defined from a learned non-parametric estimation of the statistics of the region to be segmented. Implementation details are discussed and source code is freely available as part of the 3D Slicer project. In addition, a new unified set of validation metrics is proposed. Results on artificial and real MRI images show that the algorithm performs well on large brain structures both in terms of accuracy and robustness to noise.

Color histogram equalization through mesh deformation

In this paper we propose an extension of grayscale histogram equalization for color images. For aesthetic reasons, previously proposed color histogram equalization techniques do not generate uniform color histograms. Our method will always generate an almost uniform color histogram thus making an optimal use of the color space. This is particularly interesting for pseudo-color scientific visualization. The method is based on deforming a mesh in color space to fit the existing histogram and then map it to a uniform histogram. It is a natural extension of grayscale histogram equalization and it can be applied to spatial and color space of any dimension.

A novel method for pulmonary emboli visualization from high-resolution CT images

©2004 SPIE--The International Society for Optical Engineering. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. The electronic version of this article is the complete one and can be found online at: DOI Link: http://dx.doi.org/10.1117/12.532892

Analysis of arterial subtrees affected by pulmonary emboli

Although Pulmonary Embolism (PE) is one of the most common causes of unexpected death in the U.S., it may also be one of the most preventable. Images acquired from 16-slice Computed Tomography (CT) machines of contrast-injected patients provide sufficient resolution for the localization and analysis of emboli located in segmental and sub-segmental arteries. After a PE is found, it is difficult to assess the local characteristics of the affected arterial tree without automation. We propose a method to compute characteristics of the local arterial tree given the location of a PE. The computed information localizes the portion of the arterial tree that is affected by the embolism. Our method is based on the segmentation of the arteries and veins followed by a localized tree computation at the given site. The method determines bifurcation points and the remaining arterial tree. A preliminary segmentation method is also demonstrated to locally eliminate over-segmentation of the arterial tree. The final result can then be used assess the affected lung volume and arterial supply. Initial tests revealed a good ability to compute local tree characteristics of selected sites.

A Laplace equation approach for shape comparison

In this paper we propose a principled approach for shape comparison. Given two surfaces, one to one correspondences are determined using the Laplace equation. The distance between corresponding points is then used to define both global and local dissimilarity statistics between the surfaces. This technique provides a powerful method to compare shapes both locally and globally for the purpose of segmentation, registration or shape analysis. For improved accuracy, we propose a Boundary Element Method. Our approach is applicable to datasets of any dimension and offers subpixel resolution. We illustrate the usefulness of the technique for validation of segmentation, by defining global dissimilarity statistics and visualizing errors locally on color-coded surfaces. We also show how our technique can be applied to multiple shapes comparison.

A Statistically Based Surface Evolution Method for Medical Image Segmentation: Presentation and Validation

In this paper we present a new algorithm for 3D medical image segmentation. The algorithm is fast, relatively simple to implement, and semi-automatic. It is based on minimizing a global energy defined from a learned non-parametric estimation of the statistics of the region to be segmented. Implementation details are discussed and source code is freely available as part of the 3D Slicer project. In addition, a new unified set of validation metrics is proposed. Results on artificial and real MRI images show that the algorithm performs well on large brain structures both in terms of accuracy and robustness to noise.

Low cost, high performance robot design utilizing off-the-shelf parts and the Beowulf concept, The Beobot project

Utilizing off the shelf low cost parts, we have constructed a robot that is small, light, powerful and relatively inexpensive (<